Let's go through each expression step-by-step:
1. [tex]\( (-1)^{100} \)[/tex]
- Any negative number raised to an even power results in a positive number.
- [tex]\( (-1)^{100} = 1 \)[/tex]
2. [tex]\( 17^{10} \times 0 \)[/tex]
- Any number multiplied by zero is zero.
- [tex]\( 17^{10} \times 0 = 0 \)[/tex]
3. [tex]\( (-10)^5 \)[/tex]
- A negative number raised to an odd power remains negative.
- [tex]\( (-10)^5 = -100000 \)[/tex]
4. [tex]\( 9 \times 10^2 \)[/tex]
- Multiply 9 by 100.
- [tex]\( 9 \times 10^2 = 900 \)[/tex]
5. [tex]\( (-3)^3 \times (-1)^{16} \)[/tex]
- [tex]\( (-3)^3 = -27 \)[/tex] because a negative number raised to an odd power is negative.
- [tex]\( (-1)^{16} = 1 \)[/tex] because a negative number raised to an even power is positive.
- Therefore, [tex]\( (-3)^3 \times (-1)^{16} = -27 \times 1 = -27 \)[/tex]
6. [tex]\( 7^2 \times (-1)^9 \)[/tex]
- [tex]\( 7^2 = 49 \)[/tex]
- [tex]\( (-1)^9 = -1 \)[/tex] because a negative number raised to an odd power remains negative.
- Therefore, [tex]\( 7^2 \times (-1)^9 = 49 \times -1 = -49 \)[/tex]
7. [tex]\( (-5)^2 \div (-1)^6 \)[/tex]
- [tex]\( (-5)^2 = 25 \)[/tex] because a negative number raised to an even power is positive.
- [tex]\( (-1)^6 = 1 \)[/tex]
- Therefore, [tex]\( 25 \div 1 = 25 \)[/tex]
8. [tex]\( \left( \frac{-3}{8} \right)^2 \)[/tex]
- Square both the numerator and the denominator.
- [tex]\( \left( \frac{-3}{8} \right)^2 = \frac{(-3)^2}{8^2} = \frac{9}{64} \)[/tex]
9. [tex]\( 2^2 + 3^2 \)[/tex]
- [tex]\( 2^2 = 4 \)[/tex]
- [tex]\( 3^2 = 9 \)[/tex]
- Therefore, [tex]\( 2^2 + 3^2 = 4 + 9 = 13 \)[/tex]
10. [tex]\( (-6)^2 + (-6)^2 \)[/tex]
- [tex]\( (-6)^2 = 36 \)[/tex]
- Since both are squared, it becomes [tex]\( 36 + 36 = 72 \)[/tex]
11. [tex]\( 4^1 + 4^1 + 4^1 \)[/tex]
- [tex]\( 4^1 = 4 \)[/tex]
- Therefore, [tex]\( 4^1 + 4^1 + 4^1 = 4 + 4 + 4 = 12 \)[/tex]
12. [tex]\( 4^3 \)[/tex]
- [tex]\( 4^3 = 4 \times 4 \times 4 = 64 \)[/tex]
So, the values are:
1. [tex]\( (-1)^{100} = 1 \)[/tex]
2. [tex]\( 17^{10} \times 0 = 0 \)[/tex]
3. [tex]\( (-10)^5 = -100000 \)[/tex]
4. [tex]\( 9 \times 10^2 = 900 \)[/tex]
5. [tex]\( (-3)^3 \times (-1)^{16} = -27 \)[/tex]
6. [tex]\( 7^2 \times (-1)^9 = -49 \)[/tex]
7. [tex]\( (-5)^2 \div (-1)^6 = 25 \)[/tex]
8. [tex]\( \left( \frac{-3}{8} \right)^2 = 0.140625 \)[/tex]
9. [tex]\( 2^2 + 3^2 = 13 \)[/tex]
10. [tex]\( (-6)^2 + (-6)^2 = 72 \)[/tex]
11. [tex]\( 4^1 + 4^1 + 4^1 = 12 \)[/tex]
12. [tex]\( 4^3 = 64 \)[/tex]
